This is straightforward if you know the binding site sequence -- just surround the sequence with some junk DNA that will have little effect. Make it match the GC composition of the organism you are studying (likely around 50%). Almost all binders will only bind to dsDNA, so you will need to either synthesize the other strand, or to make it double stranded with PCR. I would probably choose to make a longer fragment, perhaps 50 bp. You could make two 35 bp oligos with a 20 bp dsDNA overlap when annealed, then do a few cycles of PCR to provide extension and a 50 bp dsDNA product.